Question

please answer me fast question number 24
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Answer 1

$x ^{2} - kx + 16 = 0$

sum of roots

$\alpha + \beta = - b \div a = k \times 1 = k$

$\alpha \beta = 16$

$\alpha - \beta = \sqrt{( \alpha - \beta } ) ^{2} = \sqrt({ \alpha + \beta } ) ^{2} - 4 \alpha \beta$

$\alpha - \beta = \sqrt{(k) ^{2} - 64 } = 1$

$\alpha - \beta = 1$

k^2 -64=1

k^2 =65

k=√65